Hmm, the question is too broad to give a definitive answer. How would you describe any experience? It depends on the nature of the experience, the nature of the character, and the role of the experience in the story.
If the experience was fundamentally emotional, like a character is sinking into despair at the mess he has made of his life and suddenly decides that his only option is to turn to God for help, than I'd describe it in emotional terms. I'd have the character describe his feelings -- either in narration or in conversation with another character. If you can write emotions effectively, you could talk about his despair and sobbing and calling out to God in desperation. (Or "to the gods" or whatever. You didn't say what religion you're talking about.)
If the experience was intellectual, if the character has spent years carefully studying objective evidence and has now come to the conclusion that the weight of scientific and/or historical and/or philosophical evidence favors this religion, then I'd talk about how hard he has studied and all the evidence he has reviewed and how he has carefully considered arguments and counter-arguments.
In either case, you should consider whether you want to express approval of the character's new beliefs, disapproval, or if you want to avoid expressing any value judgement. Do you describe his experience in ways that make him sound like a reasonable, intelligent person who has come to a rational conclusion, like a raving lunatic who has gone off the deep end, or do you want to frame it in a way that leaves the reader to judge?
As with any scene in any story, you have to consider how readers will react.
A strong emotional scene can make a story powerful and appealing. Some of the best loved stories are those with powerful emotional scenes. But overdo it and readers can be turned off. I've read plenty of stories where overdone emotional scenes leave me saying, "Yeah yeah, I get it, she's sad. Why can't you just tell me she's sad and move on?" If I had a formula for how to do this right, I suppose I'd be a world-famous writer and not the dabbler that I am. :-)
Religion can be particularly touchy. If you attack a religion, you can expect people who follow that religion to be uninterested in reading your book. Why would I want to read a book that attacks me? A few such books manage to get a reputation for being controversial and important and so even opponents read them so they can give a rebuttal, but that's hard to pull off. Usually if you insult people, they just ignore you.
If you endorse or praise a religion, people who dislike that religion may similarly respond negatively. This tends to be less dramatic. I'm a Protestant, but I tend to have a favorable view of books or movies that praise other branches of Christianity, as long as they're not attacking Protestantism. I'm pretty neutral on religions that are largely dead. Like I read Greek myths without worrying that they are advocating paganism, because that's just not much of an issue today. But atheists tend to react negatively to stories that praise Christianity, and Christians tend to react negatively to stories that praise atheism.